update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_structure.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
index 4577a65b69ea451d9719d30152e3ca4865136a12..86a4259758106db83442adc285d8af1a472cc3f2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
@@ -12,48 +12,24 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/syntax/path_structure.ma".
 
 (* LIFT FOR PATH ***********************************************************)
 
 (* Constructions with structure ********************************************)
 
-lemma lift_d_empty_dx (n) (p) (f):
-      (⊗p)◖𝗱❨(↑[p]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
-#n #p @(path_ind_lift … p) -p // [ #m #l #p |*: #p ] #IH #f
-[ <lift_rmap_d_sn <lift_path_d_lcons_sn //
-| <lift_rmap_L_sn <lift_path_L_sn <IH //
-| <lift_rmap_A_sn <lift_path_A_sn <IH //
-| <lift_rmap_S_sn <lift_path_S_sn <IH //
-]
-qed.
-
-lemma lift_L_dx (p) (f):
-      (⊗p)◖𝗟 = ↑[f](p◖𝗟).
-#p @(path_ind_lift … p) -p // #m #l #p #IH #f
-<lift_path_d_lcons_sn //
-qed.
-
-lemma lift_A_dx (p) (f):
-      (⊗p)◖𝗔 = ↑[f](p◖𝗔).
-#p @(path_ind_lift … p) -p // #m #l #p #IH #f
-<lift_path_d_lcons_sn //
-qed.
-
-lemma lift_S_dx (p) (f):
-      (⊗p)◖𝗦 = ↑[f](p◖𝗦).
-#p @(path_ind_lift … p) -p // #m #l #p #IH #f
-<lift_path_d_lcons_sn //
-qed.
-
 lemma structure_lift (p) (f):
       ⊗p = ⊗↑[f]p.
-#p @(path_ind_lift … p) -p // #p #IH #f
-<lift_path_L_sn //
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <lift_path_m_sn <structure_m_sn <structure_m_sn //
+| <lift_path_L_sn <structure_L_sn <structure_L_sn //
+]
 qed.
 
 lemma lift_structure (p) (f):
       ⊗p = ↑[f]⊗p.
-#p @(path_ind_lift … p) -p //
+#p elim p -p //
+* [ #n ] #p #IH #f //
 qed.